GATE EC 1998 Electromagnetics Solution Q 12

GATE EC 1998 Electromagnetics Solution Q 12

All transmission line section in Figure, have a characteristic impedance \begin{array}{l}R_0+j0.\\\end{array} The input impedance \begin{array}{l}Z_{in}\\\end{array} equals____.

GATE EC 1998 Electromagnetics Solution feature12 - Grad Plus

(a) \begin{array}{l}\frac23R_0\\\end{array}

(b) \begin{array}{l}R_0\\\end{array}

(c) \begin{array}{l}\frac32R_0\\\end{array}

(d) \begin{array}{l}2\;R_0\\\end{array}

Ans :- (b)

Explanation

For \begin{array}{l}\lambda/4\\\end{array} line

\begin{array}{l}Z_{in1}=\frac{Z_{01}^2}{Z_{L1}}=\frac{R_0^2}{R_0\;/2}=2R_0\\\end{array}

For \begin{array}{l}\lambda/2\\\end{array} line

\begin{array}{l}Z_{in2}=Z_{L2}=2R_0\\\end{array}

For \begin{array}{l}\lambda/8\\\end{array} line

Z_L=\left(Z_{in1}\right)\parallel\left(Z_{in2}\right)=\left(2R_0\right)\parallel\left(2R_0\right) \therefore Z_L=R_0\\

So, for \lambda/8\\ line, Z_{in}=R_o. As it is terminated by a characteristic impedance.

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